The two axes divide the
plane into four sections called "quadrants". The quadrants are
labelled with Roman numerals (not Arabic numerals), starting at
the positive x-axis
and going around anti-clockwise:

Since they don't tell
me what the value of "y"
is, then y can be anything. This means that (4, y) is
not just one point! Since y can be –5,
then (4,
–5) is a valid answer.
So is (4,
–3), (4, 0), (4, 2), and (4,
4). So is any point that has x = 4:

By plotting a bunch of
points that "work", I can see that the "point" (4, y) is actually
an entire line: the line "x = 4", which
passes through two quadrants! So my answer is:

Quadrants I and
IV.

By the way, please use
standard notation. You can maybe abbreviate "Quadrant" as "Q",
but don't completely omit it; use Roman "I, II, III, IV", not
Arabic "1,
2, 3, 4"; and
use "&" or "and", not "plus" or "+".

In which quadrant
is / are the point(s) (x, y), such that
xy < 0?

This is asking me for
a description of the points (x, y), where
the coordinate x and y have values such that, when I multiply x and y together, I will get a negative number. To figure this one out, it's
probably simplest if I just pick a sample point from each quadrant and
see what I get.

In Quadrant I, I'll pick,
say, (2,
3). The product of
the coordinates is 2
× 3 = 6, which is
positive (greater than zero). Since any coordinate product in Quadrant
I will be similarly positive, then Quadrant I is not part of my answer.

In Quadrant II, I'll
pick, say, (–4,
5). The product is (–4) ×
5 = –20, which is
negative. Any other coordinate product in Quadrant II will also be negative,
so Quadrant II is part of my answer.

In Quadrant III, I'll
pick, say, (–2, –1). The product
is (–2)
× (–1) = 2, which
is positive. Any other product in Quadrant III will be positive also,
so Quadrant III is not part of my answer.

In Quadrant IV, I'll
pick, say, (3,
–4). The product
is 3 ×
(–4) = –12, which
is negative. Any other product in Quadrant IV will be negative also,
so Quadrant IV is part of my answer.

The points (x, y), with xy < 0,
lie in Quadrants II and IV.

You can use the Mathway widget below to
practice figuring out the quadrant in which a given point is located.
Try the entered exercise, or type in your own exercise. Then click the "paper-airplane" button to compare your answer to Mathway's.